Question

Imelda held a 6-inch long pencil at arm's length so that it matched the height of a tree 100 feet away. If the pencil was 24 inches from her eyes, about how tall was the tree?

Answer 1

The pencil and Imelda's arm together make a right triangle, similar to the triangle made by the tree with her arm plus the 100 feet distance. Those triangles are represented below

Where H represents the height of tree. Before we start calculating, first let's convert all the measures to the same unit. The relation between inches and feet is given below

$1ft=12in\Rightarrow\begin{cases}6in=0.5ft \\ 24in=2ft\end{cases}$

The ratio between corresponding sides on similar triangles is the same, therefore, we have the following equation

$\frac{0.5}{2}=\frac{H}{100+2}$

Solving for H, we have

$\begin{gathered} \frac{0.5}{2}=\frac{H}{100+2} \\ \frac{0.5}{2}=\frac{H}{102} \\ H=102\cdot\frac{0.5}{2} \\ H=25.5 \end{gathered}$

The height of the tree is 25.5 ft.